Birighitti started his career at the AIS before moving to Adelaide United in 2008. He made his first team debut against Queensland Roar on 17 October 2008 helping Adelaide to a 1–0 win. Aurelio Vidmar praised the young goalkeeper after the match saying "I think Birighitti played well he's got a really good future, he had big shoes to fill and I think he did an outstanding job tonight." His second successive A-League start came against Perth Glory at Hindmarsh Stadium after Adelaide's number one goalkeeper, 28-year-old Eugene Galekovic, was injured during the Asian Champions League match against FC Bunyodkor. Despite conceding the match's first goal at the near post, Birighitti played his part in the 2–1 win taking Adelaide to the top of the league table. With Galekovic again ruled out with injury Birighitti started the second leg of the 2008 AFC Champions League Final against Gamba Osaka on 12 November 2008; Adelaide lost the match 2–0. He injured his ankle after falling awkwardly in a training session on 17 December 2008 ruling him out of the remaining A-League 2008-09 season.
Newcastle Jets
On 17 January 2012 it was announced he had signed a two-year contract with A-League club Newcastle Jets starting post the 2012 AFC Champions League group stage. He quickly became the first choice goalkeeper for the Newcastle Jets, edging out Ben Kennedy and Jack Duncan. In late 2013 he signed a contract extension with the Jets until the end of the 2015–16 season. On 24 March 2014, Birighitti flew to Germany to discuss a possible transfer to Bundesliga club Bayer Leverkusen. After failing to secure a contract with Bayer Leverkusen he then came back to the Jets for the 2014–15 season. In October 2015, Birighitti was involved in an on-field collision with Sydney FC striker Shane Smeltz. Birightitti suffered multiple broken teeth and required facial surgery after the incident. He returned to action within weeks, missing only one A-League game.
Loan to Varese
On 27 January 2015, Birighitti joined Serie B club Varese on a six-month loan deal. He made his league debut for Varese in a 1–0 away loss to Vicenza on 25 April 2015.
On 18 July 2016, Birighitti joined Premier League side Swansea City on a two-year deal. After the 2016–17 season, Birighitti went on trial at Dutch side Willem II, following a lack of opportunities at Swansea.
On 11 September 2018, Birighitti joined Australian A-League side Melbourne City on a three-year deal. After a year in which he didn't play at all, Birighitti negotiated a mutual release from the remainder of his contract.
Central Coast Mariners
In August 2019, Birighitti joined Central Coast Mariners on a one-year contract.
